Speaking in Geneva on Thursday, the UN Secretary-General António Guterres said he was "deeply concerned" after US President Donald Trump cancelled a widely anticipated nuclear summit next month with North Korean leader Kim Jong-un.

"I am deeply concerned by the cancellation of the planned meeting in Singapore between the President of the United States and the leader of the Democratic Peoples Republic of Korea," Guterres said as he presented the UN's new agenda on disarmament in Geneva.

"I urge the parties to continue their dialogue to find a path to a peaceful and verifiable denuclearisation of the Korean peninsula," he added.

Deeply concerned by cancellation of meeting between President of the US and leader of the DPRK. I urge the parties to continue dialogue to find a path towards the verifiable denuclearization of the Korean Peninsula. Launch of my Disarmament Agenda today: https://t.co/Zi90o1XA6k

His comments came shortly after Trump informed Kim he was cancelling the nuclear summit, blaming "anger" and "hostility" from the North Korean regime for the collapse of the historic event.

Trump and Kim had been due to hold high-stakes talks on June 12 aimed at ridding the reclusive state of nuclear weapons, but the meeting was recently thrown into doubt as both sides raised the prospect of scrapping the discussions and traded threats.

Trump's letter came a day after North Korea attacked US Vice President Mike Pence as "ignorant and stupid."

"Sadly, based on the tremendous anger and open hostility displayed in your most recent statement, I feel it is inappropriate, at this time, to have this long-planned meeting," Trump wrote in a letter to Kim released by the White House.

The decision came as North Korea said it had "completely" dismantled its nuclear test site, in a carefully choreographed move portrayed by the isolated regime as a goodwill gesture ahead of the Singapore summit.

In his speech at Geneva University Thursday, Guterres meanwhile stressed that "the total elimination of nuclear weapons remains our priority," and warned against a burgeoning new arms race.

Asked by journalists afterwards if the developments in US-North Korea relations had nipped his new disarmament agenda in the bud, he answered in French that it was "quite the contrary".

"I think that what happened today shows the importance of the disarmament agenda," he said.

He stressed his belief that "the nuclear powers, including the United States, have an absolutely key role in establishing a credible disarmament process."

"Of course I am profoundly worried about the situation," he acknowledged.

"But I am asking the two parties to demonstrate nerves of steel so that we can ... (obtain) an objective we all share: the verifiable and peaceful denuclearisation of the Korean peninsula."

In his speech, Guterres pointed out that around 15,000 nuclear weapons remain in stockpiles around the world, and that "hundreds are ready to be launched within minutes."

"We are one mechanical, electronic or human error away from a catastrophe that could eradicate entire cities from the map," he warned.

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